STUDY OF COMPARISON OF APPLYING MODES IN RESPONSE SPECTRUM ANALYSIS

Abstract

In the response spectrum analysis, the method prescribed for seismic analysis of multi-storied buildings in IS 1893(part-1)2002, like other similar codes, is the method of combining the modal responses, followed by combining them by the SRSS or CQC to obtain the final response forces for design. This method is referred to, by the authors, as the Indirect method, since it is not the modal loads that are combined, but the modal responses. One drawback often pointed out concerning this method is that the resulting responses lose their signs in the process of combination by SRSS (or CQC). One method to overcome this is known as 'Dominant mode signage', available in few of the analysis and design packages, like STAAD.Pro and MIDAS/Gen. In this paper, a new method of analysis is being investigated, referred to by the authors, as the Direct method, where, instead of combining the modal responses by SRSS, the modal (lateral) loads itself are combined by SRSS before applying on the building model.

Full text

STUDY OF COMPARISON OF
APPLYING MODES IN
RESPONSE SPECTRUM ANALYSIS
Kiran Somasundar M1
P.G Scholar
Department of Civil Engineering
Amal Jyothi College of Engineering
Kanjirappally
kiran110493@gmail.com
Rahul Leslie2
Dy.Director
DRIQ
Kerala PWD
Trivandrum
rahul.leslie@gmail.com
Belarmin Xavier3
Assistant.Professor
Department of Civil Engineering
Amal Jyothi College of Engineering
Kanjirappally
belarminxavier@amaljyothi.ac.in
Abstract— In the response spectrum analysis, the method
prescribed for seismic analysis of multi-storied buildings in IS
1893(part-1)2002, like other similar codes, is the method of
combining the modal responses, followed by combining them by
the SRSS or CQC to obtain the final response forces for design.
This method is referred to, by the authors, as the Indirect
method, since it is not the modal loads that are combined, but the
modal responses. One drawback often pointed out concerning
this method is that the resulting responses lose their signs in the
process of combination by SRSS (or CQC). One method to
overcome this is known as 'Dominant mode signage', available in
few of the analysis and design packages, like STAAD.Pro and
MIDAS/Gen. In this paper, a new method of analysis is being
investigated, referred to by the authors, as the Direct method,
where, instead of combining the modal responses by SRSS, the
modal (lateral) loads itself are combined by SRSS before
applying on the building model.
Keywords—modes, response spectrum analysis
I. INTRODUCTION
The codal procedure recommended for Response
Spectrum Analysis is referred in this report as the „Indirect
Method‟, where the modal loads(ie, the set of lateral loads
corresponding to each mode)are applied on the structure, one
at a time and the modal forces(ie, the member forces obtained
from the analysis for each modal loads(Bending moment BM,
Shear force SF, Axial Force AF, etc )are combined by the
SRSS(Square Root of Sum of Squares hereafter referred to as
SRSS) The procedure has the drawback that, in case of
columns, in the process of combination of modal forces from
individual modes by SRSS, the interaction of AF‟s with its
corresponding BM‟s from within each modal force set is lost,
as AF‟s from all modal forces are combined, and finally the
interaction is between the combined AF‟s and combined BM‟s
Also in the process of combining by SRSS, the signs of forces
(AF and BM) are lost, ending up with positive signs for all
forces. As a probable solution to the latter (ie, loss of signs),
some of the analysis‟ software packages (eg STAAD Pro and
MIDAS) have come up with a „Dominant Mode signage‟
feature by which, after determining the forces (BM, AF, SF
etc)by SRSSing those from individual modal force sets applies
signs to those values with that of the results obtained from
analysing for modal loads corresponding to that mode
dominant in that direction Thus the results for the seismic
analysis in X direction are the modal forces from each mode in
X direction combined by SRSS and given the sign of the
modal forces of that mode which is dominant in the X
direction.
Here a new approach is being investigated where,
instead of analysis for the modal loads and SRSSing the
results, the load themselves are combined by SRSS and
applied as a single load on the structure This method, referred
to here is the „Direct method‟, is at present recommended only
for applying multi modal lateral loads for pushover analysis.
II. METHODOLOGY
A. Response Spectrum Analysis
Response spectrum analysis is performed using multi-
mode responses, where the free vibration modes are computed
using Eigen vector analysis.
The modal parameters for a structure come as pairs of Natural
Frequency f (in Hz) and Mode shape ∅ or time period T, which
is its reciprocal(in s). The modal parameters for few of the
lower frequencies are considered for further calculations (7 8 4
2, IS:1893(Part 1)-2002), based on the following.
 Modes for frequencies > 33 Hz need not be
considered
 The number of modes considered should be such that
the total mass participation factor should be at least
90%
 Missing mass correction for modes having frequency
beyond 33Hz

For the modal parameters considered, the following factors are
determined for each mode
• Mode participation factor of each mode Pk
• Mass participation factor for each mode Mk
• Spectral Acceleration coefficient (Sa/g)
The Design horizontal seismic coefficient Ah is calculated for
each mode from (6 4 2, IS:1893(Part 1)-2002)
Where,Z-Zone factor
I-Importance factor
R-Response reduction coefficient
Sa/g-Spectral Acceleration coefficient where the Horizontal
acceleration Sa/g is determined from the Response spectrum
curve (Fig 2,IS:1893(Part1)-2002)
. Figure 1.Spatial Acceleration coefficient-Period Graph
The lateral force due to the modal response (considering
the mode participation factor) is obtained for each mode of
all the modes considered The the force at each level for
each mode is calculated as (7.8.4.5 (c), IS:1893(Part 1)-
2002)
Ak -design horizontal seismic coefficient, calculated for
mode k
∅ik -mode shape value for mode k for that floor level i
Pk -mode participation factor for mode k
Wi- mass at that floor level i
B. Combination of modes
1)Indirect Method of Analysis: Consider five modes for a
building. For each of the five modes, we can calculate
respective Earthquake forces. Then for each of these
earthquake forces, we obtain respective Bending moments.
These Bending moments are SRSSed to obtain a single
Bending moment.
Mode1 Mode 2 Mode 3 Mode 4 Mode 5
For each mode we calculate earthquake forces for each
level
We get respective bending moments for each mode and are
SRSSed
2)Direct Method of Analysis:Consider five modes. For each
mode we obtain respective Earthquake forces for each
level. These forces are combined together to obtain a single
Earthquake force and bending moment is calculated for this
force.
Mode1 Mode 2 Mode 3 Mode 4 Mode 5

For each mode, respective earthquake forces are calculated
and combined by SRSSing
Bending moment is calculated for this combined
Earthquake force.
3)Dominant mode method: When activated, all modal
combination results will have the same sign as when the
dominant mode shape alone would have if it were excited
and then the scaled results were used as a static
displacements result.
C. Calculations
A lumped mass model is taken for the study having
23.57kN each.Rectangular plate of size 0.4x0.23 and
0.3x0.4 are taken for modelling.Height is 18 m with seven
floors and plate thickness of plate is 0.1m.After applying
the loads we obtain the modes shapes for each floor out of
which we select five modes.
Table 1 : Mode Shapes
Time period and frequency is also obtained from software
Table 2 : Time period and Frequency
Perio
d (sec)
0.694
0.222
0.123
0.085
0.065
Freq(Hz)
1.441
4.51
8.098
11.78
15.31
For kth mode, we should check for mass participation
Where, n = no. of levels
m = no. of modes
Table 3 : Mass participation
Mode participation factors are calculated thereafter
Table 4 : Mode Participation
Design horizontal seismic coefficient is given by,
Z = Zone factor = 0.16
I = Importance factor = 1
R = Response reduction coefficient = 3
Earthquake force is calculated finally by
Combination of modes is explained earlier to get the final
results.
Period
0.693
0.221
0.123
0.084
0.065
Sa/g
1.441
2.5
2.5
1.1273
1.0979
Ah
0.0384
0.0667
0.0667
0.03
0.0292
MODES>
1
2
3
4
5
LEVELS V
1
0
0
0
0
0
2
0.151
-0.53
0.824
-1
1
3
0.389
-1
0.861
-0.047
-0.838
4
0.58
-0.98
-0.24
0.999
0.027
5
0.763
-0.41
-1
-0.285
0.813
Mode
I
II
III
IV
V
Mk (kN)
115.5
16.31
5.424
2.686
1.237
Mode
I
II
III
IV
V
Mk(kN)
115.5
16.31
5.424
2.686
1.237

Indirect method Direct method
III. CONCLUSION
The theoretical study of different types of application of
modes gave different results. That is for the same Earthquake
Forces acting on a structure, when applied in two methods
gave different results. The advantage of the new methods (i.e.,
Direct method and Dominant mode method)will preserve the
sign of the Bending moment and gives more accurate values.
For checking the methods in an economical manner, we have
to compare these methods with a time history analysis results
and check which methods gives reinforcement Asc that is
closer in values to the reinforcement required by the time
History analysis.
IV. REFERENCES
[1] Bhopal, M , Engineer, S , Cell, D , Housing, M P , and Board, I D
(2015) “Dynamics analysis of structures subjected to earthquake ”,
International Journal of Advance Engineering and Research 11–19
[2] Fajfar, P , and Eeri, M (2000) “A Nonlinear Analysis Method for
Performance Based Seismic Design ” , Earthquake Spectra, Vol 16, No
3, pp 573-592
[3] Feng, R , Baochen, Z , and Wang, X (2015) “A Mode Contribution
Ratio Method for Seismic Analysis of Large-span Spatial Structures
”,International Journal of Steel Structures 15(4): 835-852 (2015)
[4] Moghadam, A S , and Aziminejad, A (2004) “Interaction Of Torsion
And P-Delta Effects In Tall Buildings ”,13 th World Conference on
Earthquake Engineering (799)
[5] Ravi, V S , and Lekshmi, S (2016) “Effect of Shape and Plan
Configuration on Seismic Response of Structure ( ZONE II & V ) ” ,
International Journal of Science and Research (IJSR)(7), 1135–1139
[6] Sharma, M , and Maru, S (2014) “Dynamic Analysis of Multistoried
Regular Building ‟” , Journal of Mechanical and Civil
Engineering11(1), 37–42
[7] Shehu, R (2014) “The P- Δ -Ductility Effect : Overview The Effect Of
The Second Order In The Ductile Structures ” European Scientific
Journal,143-155
[8] Veritas, D N (1985) “Modal Combination Rules For Multi Component
Earthquake Excitation”13(February 1984), Earthquake Engineering And
Structural Dynamics, Vol 13, Earthquake Engineering And Structural
Dynamics, vol 20,621-635